Course Content

Other Courses

Tribhuvan university CSIT 2074 Syllabus Mathematics I (Calculus) Old Questions 2074

Mathematics I (Calculus) - Old Questions

Question Answer Details
Syllabus Notes Old Questions Unit Wise Questions Question Bank

7. Verify Mean value theorem of f(x) = x3 − 3x + 3 for [−1,2].

5 marks
Asked in 2074

Answer

Back to Question Paper
AI Generated Answer

AI is thinking...

Official Answer

Given,

f(x) = x3-3x+3 

Since, f(x) = x3-3x+3  is continuous on [-1, 2] and f’(x) = 3x2-3 so, differentiable on (-1, 2).

Thus f(x) = x3-3x+3 satisfy the both conditions for mean value theorem. So, there exist  such that


Clearly 

Hence, mean value theorem satisfied.